is one of the Jacobi theta-functions  [1]}, [2]}. The function \(\theta _3(0, \tau )\)  is holomorphic in the upper half-plane (\(\text{Im}\tau > 0\) ) and satisfies the relations
\(\theta _3(0, \tau +1) = \theta _3(0, \tau -1),\) 
\(\theta _3(0,-1/\tau ) =(-i\tau )^{1/2}\theta _3(0, \tau ),\) 
